The tune usually used for “Maoz Tzur” is a German tune used by none other than Martin Luther HaRasha for Christian hymns.
I once spent a Shabat at Mikveh Israel, the old Sefardic congregation in Philadelphia that has been existence for over 250 years — and is famed for refusing to permit any departures from its minhagim. The tunes were very much in the style of 18th century American colonial music.
So just what *is* “Jewish” music as opposed to “goyish” music?